What are the conjugate bases of the acids HF and HClO ?

The conjugate bases are ##"F"^-## and ##"ClO"^-##.

According to the Brønsted-Lowry theory, an acid ##"HA"## donates a proton to a base ##"B"##.

Its conjugate base ##"A"^-## is the product remaining after the loss of the proton.

(from study.com)

##bb"HF"##

The equation for ##"HF"## reacting with a base ##"B"## is

##underbrace("HF")_color(red)("acid") + "B" ⇌ underbrace("F"^-)_color(red)("conjugate base") + "BH"^+##

The conjugate base is ##"F"^-##.

##bb"HClO"##

The equation for ##"HClO"## is

##underbrace("HClO")_color(red)("acid") + "B" ⇌ underbrace("ClO"^-)_color(red)("conjugate base") + "BH"^+##

The conjugate base is ##"ClO"^-##.